Linear Systems of ODEs (Mathematica Tutorial)

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

Verification of the Solution (Mathematica Tutorial)

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

$UserName (Built-in Mathematica Symbol)

$UserName gives the login name of the user who invoked the Mathematica kernel, as recorded by the operating system.

AutoMultiplicationSymbol (Built-in Mathematica Symbol)

AutoMultiplicationSymbol is an option for objects such as Cell and Notebook that specifies whether to automatically display a multiplication symbol between numbers that would ...

Storing and Tracking Palette States (Mathematica Tutorial)

Palettes can be configured to remember their previous states across front end sessions. This is useful for palettes containing multiple expandable sections, tab views, ...

Discrete & Integer Data (Mathematica Guide)

Integrated into the Mathematica system are powerful functions for analyzing large volumes of discrete and integer data—often conveniently specified using Mathematica's ...

Special Ways to Input Expressions (Mathematica Tutorial)

Mathematica allows you to use special notation for many common operators. For example, although internally Mathematica represents a sum of two terms as Plus[x,y], you can ...

ToContinuousTimeModel (Built-in Mathematica Symbol)

ToContinuousTimeModel[sys] gives the continuous-time approximation of the discrete-time TransferFunctionModel or StateSpaceModel object sys.ToContinuousTimeModel[tf, s] gives ...

ToDiscreteTimeModel (Built-in Mathematica Symbol)

ToDiscreteTimeModel[sys, \[Tau]] gives the discrete-time approximation with sampling period \[Tau] of the continuous-time StateSpaceModel or TransferFunctionModel object ...

Basic Examples of Web Services (WebServices Tutorial)

Often a web service requires using data other than a simple string. This data could be something simple like an integer or a real. Often the data is more complex and is a ...